Vol 13 Issue 1 April 2025-September 2025

Abstract: The heat equation is a fundamental partial differential equation (PDE) in mathematical physics, widely used to model the diffusion of heat in each medium over time. It arises in diverse fields such as engineering, physics, and even financial mathematics (where it models option pricing under the Black-Scholes framework). Solving the heat equation efficiently and accurately is a central problem in applied mathematics, and numerous methods have been developed to tackle it. Among these, two prominent approaches stand out: the Finite Difference Method (FDM) and the Finite Element Method (FEM). This article provides an in-depth comparison of these two methods, exploring their theoretical foundations, computational implementations, advantages, limitations, and practical applications. By the end, readers will have a clear understanding of how these methods differ and when each might be preferable.

Keywords: mathematical physics, financial mathematics, Finite Element Method (FEM).

Title: A Comprehensive Comparison of Two Methods for Solving the Heat Equation

Author: Ahmad M. D. Al-Eybani

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

Vol. 13, Issue 1, April 2025 - September 2025

Page No: 3-7

Research Publish Journals

Website: www.researchpublish.com

Published Date: 09-April-2025

Abstract: To describe nature, we must set principles! Nature working with the principle of the infinite fraction of matter, only it has just been detected by the accelerators!

Until now, the material has operated on the principle of the minimum indivisible. And the least indivisible thing is the bubbles-particles, which I described in my atomic physics and worldview! My worldview is the book prophesied by John in REVELATION!

Subatomic particles can have a charge or not. For example, neutrinos don't have!

There are well-founded suspicions that nature is heading towards the beginning of the infinite part!

Keywords: Nature working, infinite fraction, atomic physics.

Title: THE NEW NATURE WITH THE BEGINNING OF THE INFINITE PART OF MATTER

Author: ALEKOS CHARALAMPOPOULOS

International Journal of Mathematics and Physical Sciences Research  

ISSN 2348-5736 (Online)

Vol. 13, Issue 1, April 2025 - September 2025

Page No: 1-2

Research Publish Journals

Website: www.researchpublish.com

Published Date: 01-April-2025